Firing multistability, symmetry, bubbles of a Shinriki oscillator with mem-elements

Abstract In this paper, a novel memristive Shinriki oscillator is established by adding a flux-controlled memristor and a charge-controlled memcapacitor. The similar symmetry is observed with the Biolek memcapacitor model. Bubbles are also investigated with varying system parameters and initial conditions from the perspectives of cascade and location. Extreme multistability occurring with different initial conditions is clearly found in attraction basins. Different firing patterns with coexisting spiking, bursting and chaotic patterns are discussed in Shinriki oscillator. Spiking and chaotic firing with periodic coexisting large limit cycle and quiescent state are detected. In this oscillator, circle/circle buster is also observed, whose quiescent state is a small amplitude oscillation and spiking state has multiple peaks. The firing multistability of the adjusted Shinriki oscillator are implemented by a Field Programmable Gate Array (FPGA). The experimental results validate the accuracy of the numerical analysis, which shows the proposed oscillator is good for the relevant research and application.